Multilayer waveguide using a nonlinear LiNb Ta1-x O3 optical film

ABSTRACT

A multilayer waveguide having an optical film of LiN b  Ta 1-x  O 3  formed on the surface of a buffer layer or substrate of material having a nearly identical lattice structure and substantially low refractive index.

FIELD OF THE INVENTION

The invention relates to a multilayer structure for nonlinear optical thin film waveguides.

BACKGROUND OF THE INVENTION

Nonlinear optics open up a wide range of applications for the generation of new frequencies and the control of light by light. The optical power required for nonlinear optical devices can be substantially reduced by using optical waveguides. The applications of guided wave nonlinear optics include second harmonic generation, parametric devices, modulators, and nonlinear switching. The process involves the mixing of one or more optical beams over some interaaction length. The interaction efficiency is governed by the nonlinear optical response of the medium, the intensity of the interacting beams, and the distance over which phase matched mixing occurs. The first factor is a materials issue. The other two factors are optimized by guided wave geometries. Optical waveguides consist of regions of high refractive index bounded by regions of low index, thus providing strong beam confinement over long propagation distances. The size of the confinement regions is the order of the wavelength of light and strong depends on the difference in refractive index between the nonlinear opticl film and the bounding media. The distance over which the mixing occurs is limited by the propagation lobbed, that are closely related to crystal imperfection and interface structures, and by the waveguide nonuniformity.

LiNbO₃ is an attractive material for applications of nonlinear optics because of its large nonlinear susceptibilities, transparency from 350 to 4000 nm, and well developed waveguide technologies. Several methods are known to form a thin film optical waveguide using LiNbO₃. Ti-doped LiNbO₃ films on LiNbO₃ substrates or LiNbO₃ films on Mg-doped LiNbO₃ substrates have been used to form structures with different refractive indices. Although a good epitaxial structure can be achieved in this case due to nearly equal lattice constants of pure and doped-LiNbO₃, the differences in refractive index between the surface layer and underlaying substrate are quite small. For instance, the refractive index of 5-mol% MgO-doped and undoped LiNbO₃ at 630 nm is 2.192 and 2.203, respectively. See "LiNbO₃ thin-film optical waveguide grown by liquid phase epitaxy and its application to second-harmonic generation", by H. Tamada et al., J. Appl. Phys. 70, 2536 (1991). Thus a thick surface layer is required to form a waveguide, and the optical confinement is relatively poor, resulting in low guided-wave intensities and limited efficiencies of nonlinear optical interactions. Recently c-oriented epitaxial films of LiNbO₃ and LiTaO₃ have been grown on sapphire. See "Epitaxial Growth of LiNbO₃ -LiTaO₃ Thin Films on Al₂ O₃ " by T. Kanata et al., J. Appl. Phys. 62, 2989 (1987). In such cases a significant improvement in optical confinement can be achieved, because the Al₂ O₃ refractive index 1.76 is substantially lower than those of LiNbO₃ or LiTaO₃. However, the large lattice mismatch of 7.6% for LiNbO₃ or LiTaO₃ grown on Al₂ O₃ results in relatively poor crystallines and surface morphologies, as compared to the first approach. U.S. Pat. No. 5,158,823 issued Oct. 27, 1992 to Enomoto et al achieved a second harmonic wave generating device using sequential deposition of LiTaO₃ and LiNbO₃ on LiNbO₃ single crystals to form a structure of LiNbO₃ /LiTaO₃ /LiNbO₃. Lattice matching is achievable because of the similar crystal structure of LiNbO₃ and LiTaO₃, and the difference in refractive index is approximately 0.1, substantially greater than that obtained by the first approach. However, the difference in refractive index is not sufficiently high to achieve the very tight optical confinement. Moreover, the concept is not applicable to the use of LiTaO₃ for nonlinear optical devices, because the reversal of the deposition sequence with LiTaO₃ on LiNbO₃ forms a non-waveguide structure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an embodiment of the multilayer structure of the invention;

FIG. 2 is a schematic diagram of a specific embodiment of the multilayer structure of the invention;

FIG. 3 is a schematic diagram of an alternative embodiment of the invention;

FIG. 4 shows ion channeling spectra of a heteroepitaxial structure of c-oriented LiNbO₃ /MgO/LiTaO₃ ;

FIG. 5 shows ion channeling spectra of Mg₄ Nb₂ O₉ on c-oriented LiNbO₃ ; and

FIG. 6 is a x-ray diffraction pattern of a heteroepitaxial structure of c-oriented LiNbO₃ /Mg₄ Ta₂ O₉ /LiTaO₃.

SUMMARY OF THE INVENTION

It is an object of this invention to provide an optical waveguide structure having good lattice matching and pronounced differences in refractive index.

This object is achieved in a waveguide structure comprising a single crystal substrate of LiNb_(x) Ta_(1-x) O₃, an epitaxial buffer layer overlaying the substrate, and a nonlinear optical film of LiNb_(x) Ta_(1-x) O₃ grown epitaxially on the buffer layer, the buffer layer having a substantially low refractive index and a nearly identical lattice structure with respect to the LiNb_(x) Ta_(1-x) O₃ optical film so that the difference in refractive index between the buffer layer and LiNb_(x) Ta_(1-x) O₃ optical film is larger than 0:1; and the buffer layer being selected to structurally match the LiNb_(x) Ta_(1-x) O₃ with a mismatch equal to or less than 7%.

This object is also achieved in a waveguide structure comprising a single crystal substrate and a nonlinear optical film LiNb_(x) Ta_(1-x) O₃ (x=0 to 1) grown epitaxially on the substrate, the substrate having a substantially low refractive index and a nearly identical lattice structure with respect to the LiNb_(x) Ta_(1-x) O₃ optical film so that the difference in refractive index between the substrate and LiNb_(x) Ta_(1-x) O₃ optical film is larger than 0.1; and the substrate being selected to structurally match the LiNb_(x) Ta_(1-x) O₃ with a mismatch equal to or less than 7%.

It is an advantage of this invention that optical waveguides have both good lattice matching and pronounced differences in refractive indices which help to achieve very tight optical confinement.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1 a multilayer waveguide 10 in accordance with this invention is shown. The waveguide 10 includes a c-oriented single crystal of LiNb_(x) Ta_(1-x) O₃ substrate 11, an epitaxial overlaying buffer layer 13, and a nonlinear optical film of LiNb_(x) Ta_(1-x) O₃ 15. A specific embodiment of the multilayer structure is shown in FIG. 2. A waveguide 20 consists of a c-oriented single crystal substrate of LiNb_(x) Ta_(1-x) O₃ 21, an epitaxial buffer layer 23 of c-oriented Mg₄ (Nb_(x) Ta_(1-x))₂ O₉ or (111)-oriented MgO, and a c-oriented LiNb_(x) Ta_(1-x) O₃ film 25 grown epitaxially on the buffer layer. A two layer embodiment of the invention is shown in FIG. 3. The waveguide 30 includes a c-oriented single crystal of Mg₄ (Nb_(x) Ta_(1-x))₂ O₉ 31 and a c-oriented LiNb_(x) Ta_(1-x) O₃ film 33.

The substrates are c-oriented single crystals. This is a preferable orientation, because it allows easy use of d₃₃ and γ₃₃, the largest nonlinear optical and electro-optical coefficient for LiNb_(x) Ta_(1-x) O₃. However, the same concept can be applied to "x cut" and "y cut" substrates for some applications. The materials used to fabricate the heteroepitaxial layers can be doped, lightly doped or heavily doped, as long as the doping does not significantly alter their crystallinities and optical transparency.

The buffer layer 13 in FIG. 1 is (1) transparent over a wide range of wavelengths, (2) an optical film with a substantially lower refractive index than the nonlinear optical film, and (3) a single crystal film having the same rotation symmetry as that of the substrate 11 about the surface normal and the lattice constants nearly equal to those of the substrate 11. We have found that the oxides Mg₄ (Nb_(x) Ta_(1-x))₂ O₉ (x=0 to 1) and MgO provide excellent buffer layer properties and are most suitable to form waveguides with LiNbO₃ and LiTaO₃. The characteristics of those materials are listed in Table 1. Both Mg₄ Nb₂ O₉ and Mg₄ Ta₂ O₉ have the same structure as LiTaO₃, and the lattice mismatch of Mg₄ Nb₂ O₉ and Mg₄ Ta₂ O₉ to LiTaO₃ is 0.18% and 0.16% respectively. The difference in refractive index between Mg₄ (Nb_(x) Ta₁₋ x)₂ O₉ (x=0 to 1) and LiNb_(x) Ta_(1-x) O₃ is significantly larger than that between LiNbO₃ and LiTaO₃. As indicated for MgO in Table 2, although differences exist in crystal structures between MgO and LiTaO₃, they have the same oxygen ion framework in their (111) and (0001) planes with a mismatch less than 0.2%. For purposes of this disclosure, they will be considered to have similar structures. The difference in refractive index between MgO and LiTaO₃ is 0.443.

                                      TABLE 1                                      __________________________________________________________________________     Crystal Structures and Refractive Indices of                                   LiNb.sub.x Ta.sub.1-x O.sub.3, Al.sub.2 O.sub.3, and Mg.sub.4 (Nb.sub.x        Ta.sub.1-x).sub.2 O.sub.9                                                                   LiTaO.sub.3                                                                          Al.sub.2 O.sub.3                                                                     LiNbO.sub.3                                                                          Mg.sub.4 Nb.sub.2 O.sub.9                                                            Mg.sub.4 Ta.sub.2 O.sub.9                 Structure    trigonal                                                                             trigonal                                                                             trigonal                                                                             trigonal                                                                             trigonal                                  __________________________________________________________________________     a(nm)        0.51530                                                                              0.47630                                                                              0.51494                                                                              0.51624                                                                              0.51611                                   Mismatch to LiTaO.sub.3 (%)                                                                 0.00  -7.57 -0.07 0.18  0.16                                      c(nm)        1.3755                                                                               1.3003                                                                               1.3862                                                                               1.40240                                                                              1.40435                                   Mismatch to LiTaO.sub.3 (%)                                                                 0.00  -5.47 0.78  1.96  2.10                                      n(refractive 2.180(n.sub.e)                                                                       1.760 2.20(n.sub.e)                                                                        1.95 at                                                                              1.85                                      index at 633 2.175(n.sub.o)                                                                             2.28(n.sub.o)                                                                        546.1 nm                                        nm)                                                                            n-n(LiTaO.sub.3)                                                                            0.00  -0.42 0.020(n.sub.e)                                                                       -0.23 -0.33                                                              0.105(n.sub.o)                                        __________________________________________________________________________

                  TABLE 2                                                          ______________________________________                                         Crystal Structures and Refractive Indices of                                   LiNb.sub.x Ta.sub.1-x O.sub.3 and MgO                                                       LiTaO.sub.3                                                                             LiNbO.sub.3                                                                             MgO                                             ______________________________________                                         Symmetry of oxygen                                                                            6-fold     6-fold   6-fold                                      sublattice                                                                     Distance between                                                                               2.974       2.972  2.978                                       neighboring oxygen                                                             atoms                                                                          Mismatch to LiTaO.sub.3 (%)                                                                   0.00       -0.07    0.13                                        n(refractive index)                                                                           2.180(n.sub.e)                                                                            2.20(n.sub.e)                                                                           1.737                                       at 633 nm      2.175(n.sub.o)                                                                            2.28(n.sub.o)                                        n-n(LiTaO.sub.3)                                                                              0.00        0.020(n.sub.e)                                                                         -0.443                                                                 0.105(n.sub.o)                                      ______________________________________                                    

The buffer layer can be grown epitaxially by many conventional manners, such as laser ablation, sputtering, or chemical vapor deposition. It is necessary that the buffer attains a sufficient thickness, so that the strength of the evanescent tail of the mode propagating in the nonlinear optical film is negligible at the substrate-buffer layer interface to prevent guided wave loss. A sufficient thickness ranges from 200 to 3000 nm, preferably 400 to 1000 nm.

The overlaying nonlinear optical film of LiNb_(x) Ta_(1-x) O₃ can be grown by any conventional methods, such as rf-sputtering, laser ablation or metal organic chemical vapor deposition. A sufficient thickness ranges from 100 to 3000 nm, preferably 400 to 1000 nm.

EXAMPLES

Polycrystalline Mg₄ Nb₂ O₉ or Mg₄ Ta₂ O₉ targets were prepared using calcined reagent-grade MgO and Nb₂ O₅ or Ta₂ O₅. Samples were pelletized under a pressure of 5000 psi, and sintered in air in a platinum crucible at temperatures of 1400° C. and 1500° C. for Mg₄ Nb₂ O₉ and Mg₄ Ta₂ O₉, respectively. C-oriented LiNbO₃ wafers were used as substrates for epitaxial growth of MgO, Mg₄ Nb₂ O₉ or Mg₄ Ta₂ O₉ films. After a conventional cleaning in toluene, 2-propanol, and deionized water, the wafers were annealed in air at 700° C. for 1 hour prior to being loaded in a chamber for deposition.

MgO was then deposited on LiNbO₃ by electronbeam evaporation. The deposition process was carried out at 3×10⁻⁸ Torr without introducing additional oxygen into the system. The substrate was heated by a radiative heater consisting of tantalum wires. The deposition was carried out at 400° C.-550° C. and at 0.05-0.15 nm/s with a total thickness of 300-500 nm.

Mg₄ Nb₂ O₉ or Mg₄ Ta₂ O₉ films were grown by pulsed laser ablation. A laser pulse energy of 300-360 mJ with a 30 ns duration and a pulse rate of 4Hz was generated by a KrF excimer laser. The beam was focused to a 5 mm² spot onto a target of polycrystalline Mg₄ Nb₂ O₉ or Mg₄ Ta₂ O₉. The LiNbO₃ substrate was located 6 cm from the target and heated to 650° C.-750° C. by a resistive heater. The temperature was monitored by a thermocouple attached to an inner wall of the heater block. The deposition was carried out at a rate of 0.1 nm/pulse under an oxygen pressure of 100 m Torr. After 4000-6000 pulses the oxygen pressure was raised to 150 Torr, and the sample was cooled to room temperature.

LiNbO₃ and LiTaO₃ films were deposited by pulsed laser deposition on LiNbO₃ with an intermediate buffer layer of MgO, Mg₄ Nb₂ O₉ or Mg₄ Ta₂ O₉. The deposition conditions are similar to those for Mg₄ Nb₂ O₉ or Mg₄ Ta₂ O₉, except that a relatively low deposition temperature of 600°-650° C. was used.

The samples were characterized by x-ray diffraction. The distribution of c-axis orientations relative to the normal of the substrate surface was determined by x-ray rocking curve analysis, and the feature of in-plane orientation was examined by x-ray pole figure analysis. These techniques are well known and are illustrated by B. D. Cullity, Elements of x-ray Diffraction (Addison-Wesley, Reading, MA).

EXAMPLE 1

A thin film of MgO with a thickness of 400 nm was deposited on a c-oriented LiNbO₃ substrate at 550° C. by e-beam evaporation, and a layer of LiTaO₃ with a thickness of 500 nm was then deposited on the MgO coated LiNbO₃ substrate at 650° C. by laser ablation.

The standard 2-theta diffraction pattern taken from a MgO film on LiNbO₃ revealed only the MgO(111) and LiNbO₃ (006) diffraction peaks. The full width at half maximum (FWHM) of the MgO(111) rocking curve measured about 0.5°. Epitaxial growth of MgO on LiNbO₃ was verified by x-ray pol figure analysis. The pole figure taken from the (200) peak of the MgO overlayer exhibits three spot-like pole densities showing three-dimensional alignment. A comparison of the results obtained from MgO and that from the underlaying LiNbO₃ indicates that a single-crystal (111)-oriented MgO film was grown on c-oriented LiNbO₃ with an in-plane alignment of MgO(110) parallel to LiNbO₃ (110).

LiTaO₃ films prepared on (0001)LiNbO₃ /MgO were shiny and smooth. The good crystal quality of the LiTaO₃ film was verified by ion channeling measurements. FIG. 4 shows backscattering spectra with He ions at both a random and a (0001)-oriented incidence. The minimum yield of the LiTaO₃ film was determined to be about 0.2. The crystallinity can be further improved by optimizing the experimental conditions for MgO deposition. The (001) LiNbO₃ /MgO/LiTaO₃ was optically characterized by the m-line spectroscopic measurements and guided optical waves were found in the LiTaO₃ film.

EXAMPLE 2

A thin film of MgO with a thickness of 400 nm was deposited on a c-oriented LiNbO₃ substrate at room temperature, and then annealed at 705° C. for 60 min in O₂. X-ray analysis reveals that besides the peaks from MgO(111) and LiNbO₃ (0006), several lines appear in the diffraction pattern, corresponding to a phase of Mg₄ Nb₂ O₉. The full width at half maximum of the MgO(111) and Mg₄ Nb₂ O₉ (004) rocking curves measured about 1.4° and 0.5°, respectively. These results indicate that Mg₄ Nb₂ O₉ is readily grown on LiNbO₃ and LiTaO₃ to form an epitaxial film. The structure information from JCPDS-ICDD 38-1458 and 38-1459 further supports our data. See for example Powder Diffraction File (International Centre for Diffraction Data, USA, 1992). Thus, the following experiments were carried out to form the heteroepitaxial structures LiNbO₃ /Mg₄ Nb₂ O₉ /LiTaO₃ and LiNbO₃ /Mg₄ Ta₂ O₉ /LiTaO₃. Our refractive index measurements on Mg₄ Nb₂ O₉ and Mg₄ Ta₂ O₉ indicate that both materials can be used as bounding media to form optical waveguides with LiNbO₃ or LiTaO₃.

EXAMPLE 3

A thin film of Mg₄ Nb₂ O₉ with a thickness of 500 nm was deposited on a c-oriented LiNbO₃ substrate at 750° C. by laser ablation. The standard 2-theta diffraction pattern taken from a Mg₄ Nb₂ O₉ film on LiNbO₃ reveals only the (0002), (0004) and (0006) diffraction peaks from Mg₄ Nb₂ O₉ and the (0006) peak from LiNbO₃. Ion channeling spectra in FIG. 5 show a highly oriented Mg₄ Nb₂ O₉ film on LiNbO₃ with a minimum channeling yield of 9%. Since no data are available on refractive indices of Mg₄ Nb₂ O₉, ellipsometric measurements were carried out on a Mg₄ Nb₂ O₉ film grown on LiNbO₃. The refractive index of Mg₄ Nb₂ O₉ at 546.1 nm was determined to be about 1.95. Since Mg₄ Nb₂ O₉ is transparent and has a lower refractive index than of LiTaO₃, a thin-film waveguide is formed in the structure of LiNbO₃ /Mg₄ Nb₂ O₉ /LiTaO₃. The minimum channeling yield of the LiTaO₃ film was determined to be 12%.

EXAMPLE 4

A thin film of Mg₄ Ta₂ O₉ with a thickness of 500 nm was deposited on a c-oriented LiTaO₃ substrate at 750° C., and then a thin film of LiTaO₃ with a thickness of 500 nm was grown on the Mg₄ Ta₂ O₉ coated LiNbO₃ substrate. The standard 2-theta diffraction pattern taken from a Mg₄ Nb₂ O₉ film on LiNbO₃ reveals only the (0002), (0004) and (0006) diffraction peaks from Mg₄ Ta₂ O₉ and the (0006) peak from LiNbO₃. Ellipsometric measurements were carried out on a Mg₄ Ta₂ O₉ film grown on LiNbO₃, and a refractive index of 1.85 at 633 nm was determined. The difference in refractive index between LiTaO₃ and Mg₄ Ta₂ O₉ is approximately 0.3 or three times higher than that between LiTaO₃ and LiNbO₃,so that 500 nm of LiTaO₃ on 500 nm of Mg₄ Ta₂ O₉ is sufficient to form a waveguide with an optical loss less than 0.2dB/cm.

The standard 2-theta diffraction pattern in FIG. 6 taken from a heteroepitaxial structure of LiNbO₃ /Mg₄ Ta₂ O₉ /LiTaO₃ exhibits approximately the same profile as that observed for LiNbO₃ /Mg₄ Ta₂ O₉. The LiTaO₃ and LiNbO₃ reflection lines overlap because of their identical crystal structure and almost equal lattice parameter. The minimum channeling yield of LiTaO₃ film was determined to be 7.8%, indicating a high degree of epitaxy.

The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention.

PARTS LIST

10: Waveguide

11: Substrate

13: Buffer Layer

15: Film

20: Waveguide

21: Substrate

23: Buffer Layer

25: Film

30: Waveguide

31: Crystal

33: Film 

I claim:
 1. A multilayer waveguide comprising:a c-oriented single crystal substrate of LiNb_(x) Ta_(1-x) O₃ (x=0 to 1); an epitaxial buffer layer having a thickness of from 200 to 1000 nm overlaying the substrate, and a nonlinear optical thin film LiNb_(x) Ta_(1-x) O₃ having a thickness of 200 to 1000 nm grown epitaxially on the buffer layer; the buffer layer providing a substantially low refractive index and having a nearly identical lattice structure with respect to the LiNb_(x) Ta_(1-x) O₃ substrate so that the difference in refractive index between the buffer layer and LiNb_(x) Ta_(1-x) O₃ is larger than 0.1; and the buffer layer being selected to structurally match the LiNb_(x) Ta_(1-x) O₃ substrate with a mismatch equal to or less than 7%.
 2. A waveguide structure comprising:a single crystal substrate and a nonlinear optical film LiNb_(x) Ta_(1-x) O₃ (x=0 to 1) grown epitaxially on the substrate; the substrate having a substantially low refractive index and a nearly identical lattice structure with respect to the LiNb_(x) Ta_(1-x) O₃ optical film so that the difference in refractive index between the substrate and LiNb_(x) Ta_(1-x) O₃ optical film is larger than 0.1; and the substrate being selected to structurally match the LiNb_(x) Ta_(1-x) O₃ with a mismatch equal to or less than 7%.
 3. A structure according to claim 1 wherein said buffer layer is MgO.
 4. A structure according to claim 1 wherein said buffer layer is Mg₄ (Nb.sub. x Ta_(1-x))₂ O₉ (x=0 to 1).
 5. A structure according to claim 2 wherein said substrate is Mg₄ (Nb.sub. x Ta_(1-x))₂ O₉ (x=0 to 1).
 6. A multilayer waveguide comprising:(a) a c-oriented single crystal substrate of LiNb_(x) Ta_(1-x) O₃ ; (b) an epitaxial buffer layer of c-oriented Mg₄ (Nb₄ Ta_(1-x))₂ or (111)-oriented MgO having a thickness of 200 to 1000 nm; (c) a c-oriented single crystal optical film of LiNb_(x) Ta_(1-x) O₃ (x=0 to 1) and having a thickness of 200 to 1000 nm; and (d) the buffer layer providing a substantially low refractive index and having a nearly identical lattice structure with respect to the LiNb_(x) Ta_(1-x) O₃ so that the difference in refractive index between the buffer layer and LiNb_(x) Ta_(1-x) O₃ is larger than 0.1, and the mismatch of the buffer to LiNb_(x) Ta_(1-x) O₃ is equal to or less than 7%.
 7. A waveguide structure according to claim 3 comprising a single crystal substrate of LiNbO₃ and a nonlinear optical film of LiNbO₃ epitaxially grown on the buffer layer.
 8. A waveguide structure according to claim 3 comprising a single crystal substrate of LiNbO₃ and a nonlinear optical film of LiTaO₃ epitaxially grown on the buffer layer.
 9. A waveguide structure according to claim 4 comprising a single crystal structure of LiNbO₃, an epitaxial buffer layer of Mg₄ Nb₂ O₉ overlaying the substrate, and a nonlinear optical film of LiNbO₃ epitaxially grown on the buffer layer.
 10. A waveguide structure according to claim 4 comprising a single crystal substrate of LiNbO₃, an epitaxial buffer layer of Mg₄ Nb₂ O₉ overlaying the substrate, and nonlinear optical film of LiTaO₃ epitaxially grown on the buffer layer.
 11. A waveguide structure according to claim 4 comprising a single crystal of LiNbO₃, an epitaxial buffer layer of Mg₄ Ta₂ O₉ overlaying the substrate, and a nonlinear optical film of LiNbO₃ epitaxially grown on the buffer layer.
 12. A waveguide structure according to claim 4 comprising a single crystal substrate of LiNbO₃, an epitaxial buffer layer of Mg₄ Ta₂ O₉ overlaying the substrate, and a nonlinear optical film of LiTaO₃ epitaxially grown on the buffer layer.
 13. A waveguide structure according to claim 5 comprising a single crystal substrate of Mg₄ Nb₂ O₉ and a nonlinear optical film of LiNbO₃ epitaxially grown on the substrate.
 14. A waveguide structure according to claim 5 comprising a single crystal substrate of Mg₄ Nb₂ O₉ and a nonlinear optical film of LiTaO₃ epitaxially grown on the substrate.
 15. A waveguide structure according to claim 5 comprising a single crystal substrate of Mg₄ Ta₂ O₉ and a nonlinear optical film of LiNbO₃ epitaxially grown on the substrate.
 16. A waveguide structure according to claim 5 comprising a single crystal substrate of Mg₄ Ta₂ O₉ and a nonlinear optical film of LiTaO₃ epitaxially grown on the substrate. 